SOS-based policy iteration for H∞ control of polynomial systems with uncertain parameters

2022 ◽  
pp. 1-47
Author(s):  
Sajjad Pakkhesal ◽  
Saeed Shamaghdari
Keyword(s):  
Polynomial Systems ◽  
Policy Iteration ◽  
Uncertain Parameters

Robust stabilisation of polynomial systems with uncertain parameters

2010 ◽  
Vol 41 (5) ◽  
pp. 575-584 ◽  
Author(s):  
Francesc Pozo ◽  
José Rodellar
Keyword(s):  
Polynomial Systems ◽  
Uncertain Parameters

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

Trajectory Tracking Control Applied to an Electro-Hydraulic Actuator With Uncertain Parameters.

2019 ◽  
Author(s):  
Josiel Gouvêa ◽  
Carlos Alberto Correia ◽  
Alessandro Zachi ◽  
Wallace Moreira Bessa
Keyword(s):  
Trajectory Tracking ◽  
Tracking Control ◽  
Uncertain Parameters ◽  
Hydraulic Actuator ◽  
Trajectory Tracking Control
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